The frog model with death revisited
Samyah Ahmed, Matthew Junge
TL;DR
This paper investigates the frog model with death and drift on a $d$-ary tree, demonstrating that recurrence probability can be positive and is not monotone with respect to the drift parameter.
Contribution
It revisits the frog model with death, establishing non-monotonicity of recurrence probability in the drift parameter on $d$-ary trees.
Findings
Recurrence probability can be positive with certain drift values.
Recurrence probability is not monotone in the drift parameter.
Provides new insights into the behavior of the frog model with death.
Abstract
We prove that the probability the frog model with death and drift on the -ary tree is recurrent can be made positive and thus is not monotone in the drift parameter.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Markov Chains and Monte Carlo Methods